A dynamic epistemic characterization of backward induction without counterfactuals
AbstractThe analysis of rational play in dynamic games is usually done within a static framework that specifies a player's initial beliefs as well as his disposition to revise those beliefs conditional on hypothetical states of information. We suggest a simpler approach, where the rationality of a player's choice is judged on the basis of the actual beliefs that the player has at the time he has to make that choice. We propose a dynamic framework where the set of "possible worlds" is given by state-instant pairs (w,t). Each state w specifies the entire play of the game and, for every instant t, (w,t) specifies the history that is reached at that instant (in state w). A player is said to be active at (w,t) if the history reached in state w at date t is a decision history of his. At every state-instant pair (w,t) the beliefs of the active player provide an answer to the question "what will happen if I take action a", for every available action a. A player is said to be rational at (w,t) if either he is not active there or the action he ends up taking at state w is "optimal" given his beliefs at (w,t). We provide a characterization of backward induction in terms of the following event: the first mover (i) is rational and has correct beliefs, (ii) believes that the active player at date 1 is rational and has correct beliefs, (iii) believes that the active player at date 1 believes that the active player at date 2 is rational and has correct beliefs, etc. Thus our epistemic characterization does not rely on dispositional belief revision or on (objective or subjective) counterfactuals.
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Bibliographic InfoPaper provided by University of California, Davis, Department of Economics in its series Working Papers with number 122.
Date of creation: 18 Mar 2012
Date of revision:
Perfect-information game; backward induction; dynamic interactive beliefs; rationality; Kripke frame;
Other versions of this item:
- Bonanno, Giacomo, 2013. "A dynamic epistemic characterization of backward induction without counterfactuals," Games and Economic Behavior, Elsevier, vol. 78(C), pages 31-43.
- C7 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory
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